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http://hdl.handle.net/11320/5490
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Pole DC | Wartość | Język |
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dc.contributor.author | Futa, Yuichi | - |
dc.contributor.author | Shidama, Yasunari | - |
dc.date.accessioned | 2017-05-16T09:30:38Z | - |
dc.date.available | 2017-05-16T09:30:38Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Formalized Mathematics, Volume 24, Issue 1, pp. 49-68 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/5490 | - |
dc.description.abstract | In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9]. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.subject | ℤ-lattice | - |
dc.subject | Gram matrix | - |
dc.subject | integral ℤ-lattice | - |
dc.subject | positive definite ℤ-lattice | - |
dc.title | Lattice of ℤ-module | - |
dc.type | Article | - |
dc.identifier.doi | 10.1515/forma-2016-0005 | - |
dc.description.Affiliation | Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan | - |
dc.description.Affiliation | Shidama Yasunari - Shinshu University Nagano, Japan | - |
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dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | - |
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dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17. | - |
dc.description.references | Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. | - |
dc.description.references | Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. | - |
dc.description.references | Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. | - |
dc.description.references | Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. ℤ-modules. Formalized Mathematics, 20(1):47-59, 2012. doi:10.2478/v10037-012-0007-z. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of ℤ-module. Formalized Mathematics, 20(3):205-214, 2012. doi:10.2478/v10037-012-0024-y. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, and Yasunari Shidama. Torsion ℤ-module and torsion-free ℤ-module. Formalized Mathematics, 22(4):277-289, 2014. doi:10.2478/forma-2014-0028. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Matrix of ℤ-module. Formalized Mathematics, 23(1):29-49, 2015. doi:10.2478/forma-2015-0003. | - |
dc.description.references | A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4), 1982. | - |
dc.description.references | Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective. The International Series in Engineering and Computer Science, 2002. | - |
dc.description.references | Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990. | - |
dc.description.references | Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2016, Volume 24, Issue 1 |
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